Causal Structural Learning from Time Series: A Convex Optimization Approach

TL;DR

This paper introduces a convex optimization-based method for causal structural learning from time series data, leveraging a variational inequality formulation to improve structure recovery with theoretical guarantees and superior empirical performance.

Contribution

It presents a novel convex optimization approach for causal structural learning from time series, utilizing a VI formulation and providing non-asymptotic recovery guarantees.

Findings

Proposes a data-adaptive linear method for causal structure learning.

Establishes non-asymptotic recovery guarantees for the approach.

Demonstrates superior performance over existing methods in numerical experiments.

Abstract

Structural learning, which aims to learn directed acyclic graphs (DAGs) from observational data, is foundational to causal reasoning and scientific discovery. Recent advancements formulate structural learning into a continuous optimization problem; however, DAG learning remains a highly non-convex problem, and there has not been much work on leveraging well-developed convex optimization techniques for causal structural learning. We fill this gap by proposing a data-adaptive linear approach for causal structural learning from time series data, which can be conveniently cast into a convex optimization problem using a recently developed monotone operator variational inequality (VI) formulation. Furthermore, we establish non-asymptotic recovery guarantee of the VI-based approach and show the superior performance of our proposed method on structure recovery over existing methods via extensive numerical experiments.